Euler solution using adaptive Cartesian grid with a gridless boundary treatment

A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indi- cate the developed method is reasonable for complex flows.     

复杂无粘流场数值模拟的矩形/三角形混合网格技术

建立了一套模拟复杂无粘流场的矩形／三角形混合网格技术，其中三角形仅限于物面附近，发挥非结构网格的几何灵活性，以少量的网格模拟复杂外型；同时在以外的区域采用矩形结构网格，发挥矩形网格计算简单快速的优势，有效地克服全非结构网格计算方法需要较大内存量和较长ＣＰＵ时间的不足．混合网格系统由修正的四分树方法生成．将ＮＮＤ有限差分与ＮＮＤ有限体积格式有机地融合于混合网格计算，消除了全矩形网格模拟曲边界的台阶效应，同时保证了网格间的通量守恒．数值实验表明本方法在模拟复杂无粘流场方面的灵活性和高效性．     

动态混合网格生成及隐式非定常计算方法

建立了一种基于动态混合网格的非定常数值计算方法. 混合网格由贴体的四边形网格、外场 的多层次矩形网格和中间的三角形网格构成. 当物体运动时，贴体四边形网格随物体运动而 运动，而外场的矩形网格保持静止，中间的三角形网格随之变形；当物体运动位移较大，导 致三角形网格的质量降低，甚至导致网格相交时，在局部重新生成网格. 新网格上的物理量 由旧网格上的物理量插值而得. 为了提高计算效率，采用了双时间步和子迭代相结合的隐式 有限体积格式计算非定常Navier-Stokes方程. 子迭代采用高效的块LU-SGS方法. 利用该 方法数值模拟了NACA0012振荡翼型的无黏和黏性绕流，得到了与实验和他人计算相当一致 的结果.     

An efficient reduced-order modelling approach based on fluid eigenmodes and boundary element method

This paper presents an efficient reduced-order modelling approach based on the boundary element method. In this approach, the eigenvalue problem of the unsteady flows is defined based on the unknown wake singularities. By constructing this reduced-order model, the body quasi-static eigenmodes are removed from the eigensystem and it is possible to obtain satisfactory results without using the static correction technique when enough eigenmodes are used. In addition to the conventional method, eigenanalysis and reduced-order modelling of unsteady flows over a NACA 0012 airfoil, a wing with NACA 0012 section and a wing–body combination are performed using the proposed reduced order modelling (ROM) method. Numerical examples are presented that demonstrate the accuracy and computational efficiency of the present method.     

A hybrid building‐block and gridless method for compressible flows

A hybrid building‐block Cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries. In this method, a Cartesian mesh based on a building‐block grid is used as a baseline mesh to cover the computational domain, while the boundary surfaces are represented using a set of gridless points. This hybrid method combines the efficiency of a Cartesian grid method and the flexibility of a gridless method for the complex geometries. The developed method is used to compute a number of test cases to validate the accuracy and efficiency of the method. The numerical results obtained indicate that the use of this hybrid method leads to a significant improvement in performance over its unstructured grid counterpart for the time‐accurate solution of the compressible Euler equations. An overall speed‐up factor from six to more than one order of magnitude and a saving in storage requirements up to one order of magnitude for all test cases in comparison with the unstructured grid method are demonstrated. Copyright © 2008 John Wiley & Sons, Ltd.     

高雷诺数下求解NS方程的无网格算法

提出了一种适合高雷诺数NS方程求解的隐式无网格算法。针对高雷诺数粘性流动的特点,在附面层内的粘性影响区域采用法向层次推进布点的方法形成离散点云,在附面层外的计算区域内实行填充式布点的方法形成离散点云。根据附面层内外点云的不同构造特点,推导出运用格林公式和最小二乘曲面拟合方法求取空间导数的统一形式,在此基础上运用AUSM _up格式求得数值通量,并引入BL湍流模型对雷诺平均NS方程的湍流应力项进行封闭。时间推进格式方面,采用了计算效率较高的隐式高斯-赛德尔迭代算法。为了验证本文方法的计算精度和鲁棒性,对NACA0012翼型低速流动、RAE2822翼型跨音速绕流和二维圆柱的分离流动进行了数值模拟。     

Numerical solution of the unsteady Euler equations for airfoils using approximate boundary conditions

This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary rectilinear grids. Boundary conditions on the surface of an airfoil are implemented by using their first-order expansions on the mean chord line. The method is not restricted to flows with small disturbances since there are no restrictions on the mean angle of attack of the airfoil. The mathematical formulation and the numerical implementation of the wall boundary conditions in a fully implicit time-accurate finite-volume Euler scheme are described. Unsteady transonic flows about an oscillating NACA 0012 airfoil are calculated. Computational results compare well with Euler solutions by the full boundary conditions on a body-fitted curvilinear grid and published experimental data. This study establishes the feasibility for computing unsteady fluid-structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in saving computer time and program design since it does not require the generation and implementation of time-dependent body-fitted grids.     

Chimera technique for transporting disturbances

The Chimera technique for moving grids is used to take into account nonhomogeneous unsteady inflow conditions in the simulation of aerodynamic flows. The method is applied to simulate the transport of a large‐scale vortex by a mean velocity field over a large distance, where it finally interacts with an airfoil. The Chimera approach allows one to resolve the vortex on a fine grid, whereas the unstructured background grid covering most of the computational domain can be much coarser. This method shows the same low numerical dissipation as a simulation on a globally fine grid. Several precursor tests are performed with a finite modified analytical Lamb–Oseen type vortex to study the influence of spatial and temporal resolution and the employed numerical scheme. Then, the interaction of an analytical vortex with a NACA0012 airfoil and with an ONERA‐A airfoil near stall is studied. Finally, a realistic vortex is generated by a ramping airfoil and is transported on a moving Chimera block and then interacts with a two‐element airfoil, which allows one to simulate a typical setup for a gust generator in aerodynamic facilities. Copyright © 2012 John Wiley & Sons, Ltd.     

非定常流动的快速拉格朗日涡方法数值模拟

采用快速拉格朗日涡方法数值模拟有复杂旋涡运动的非定常流动. 利用离散涡元模拟旋涡的产生、聚集和输送过程. 拉格朗日描述法用来计算离散涡元的移动,而移动速度则利用广义毕奥-萨伐尔公式结合快速多极子展开法计算,修正的涡半径扩散模型用来模拟离散涡元的黏性扩散. 突然起动圆柱和大攻角下突然起动翼型的非定常有涡流动的数值模拟,及其与试验结果的对比验证了方法的有效性. 另外,大攻角下突然起动翼型的计算结果给出了翼型起动后吸力面旋涡的产生、发展,周期性非定常流动的形成,以及尾流旋涡结构等一些重要的流动特征.[关键词] 非定常流有涡流动快速涡方法      

A sensitivity equation method for fast evaluation of nearby flows and uncertainty analysis for shape parameters

This paper presents the application of the continuous sensitivity equation method (CSEM) to fast evaluation of nearby flows and to uncertainty analysis for shape parameters. The flow and sensitivity fields are solved using an adaptive finite-element method. A new approach is presented to extract accurate flow derivatives at the boundary, which are needed in the shape sensitivity boundary conditions. Boundary derivatives are evaluated via high order Taylor series expansions used in a constrained least-squares procedure. The proposed method is first applied to fast evaluation of nearby flows: the baseline flow and sensitivity fields around a NACA 0012 airfoil are used to predict the flow around airfoils with nearby shapes obtained by modifications of the thickness (NACA 0015), the angle of attack and the camber (NACA 4512). The method is then applied to evaluate the influence of geometrical uncertainties on the flow around a NACA 0012 airfoil.     

Design optimization of unsteady airfoils with continuous adjoint method

In this paper, a new unsteady aerodynamic design method is presented based on the Navier-Stokes equations and a continuous adjoint approach. A basic framework of time-accurate unsteady airfoil optimization which adopts time-averaged aerodynamic coefficients as objective functions is presented. The time-accurate continuous adjoint equation and its boundary conditions are derived. The flow field and the adjoint equation are simulated numerically by the finite volume method (FVM). Feasibility and accuracy of the approach are perfectly validated by the design optimization results of the plunging NACA0012 airfoil.     

非结构动网格在可动边界问题中的应用研究

本文对用于非结构动网格生成的弹簧近似方法进行了研究。通过采用顶点弹簧方法,分析研究了弹簧倔强系数的取值,同时通过引入挤压倔强系数和边界修正,对标准弹簧近似方法进行了改进。改进后的方法可以大大提高网格变形能力和网格质量。应用本文发展的非结构动网格生成方法并通过耦合求解基于(ArbitraryLagrangian-Eulerian ALE)描述的Euler方程,模拟了谐和振动NACA0012翼型及M6机翼的跨音速绕流,计算结果与参考文献提供的结果及实验结果吻合良好。     

翼型、机翼非定常运动模式下动态数值模拟

基于RANS方程,通过刚性动网格技术实现对翼型和机翼典型运动模式的描述,采用双时间推进方法和Roe空间离散格式对流场求解,构建了一个非定常气动计算平台;以NACA0012翼型为算倒进行了动态数值模拟可信度验证。数值模拟结果与试验数据吻合较好,升力和俯仰力矩的最大计算误差分别为3％和10％,表明了该平台的可靠性。另外,还数值模拟了M6机翼的动态非定常流场,并分析了两种湍流模型对非定常流场激波的捕捉能力。结果表明非定常流动中S-A湍流模型对激波的捕捉较B-L模型更敏感。文中开发的非定常计算平台对进一步解决三维复杂流场的流动问题有很高的工程应用价值。     

基于自适应直角网格的二维全速势方程有限体积解法A finite volume method for 2D Full-Potential equation on adaptive Cartesian grids

为满足亚声速和跨声速飞机概念设计中快速气动计算的需求,研究和发展一种基于自适应直角网格的非线性全速势方程有限体积解法。要点如下。（1）在几何自适应直角网格的基础上,使用结合单元融合的网格切割算法处理物面边界,提出一种修正非贴体切割网格的方法。（2）采用隐式格式结合GM RES算法求解该非线性位流方程,针对流场的自适应来捕捉激波。（3）采用镜像法处理物面边界处的无穿透条件,并提出解析的方法来修正镜像单元的值。（4）针对直角网格的特点,提出在库塔线上插入库塔单元的方法施加库塔条件。NACA0012翼型绕流的算例结果表明,该方法用于亚声速和跨声速气动计算能得到令人满意的结果,且自动化程度高、收敛速度快。     

Experimental and numerical investigation on sound generation from airfoil-flow interaction

Aerodynamic noise due to interaction between incoming turbulence and rotating blades is an important component in the wind turbine noise. The rod-airfoil configuration is used to investigate the interactive phenomenon experimentally and numerically. Distribution of unsteady pressure on the airfoil surface is measured for different rod positions and airfoil attack angles. Two National Advisory Committee for Aeronatics (NACA) airfoils, NACA0012 and NACA0018, and two wind turbine airfoils, S809 and S825 are investigated. In addition, for low angles of attack, the flow field around the airfoil's leading edge is investigated with the particle image velocimetry (PIV). The experimental results indicate that unsteady pressure disturbances on the airfoil surface are related to the rod vortex shedding. Meanwhile, the interaction flow field of the rod and NACA0012 airfoil is simulated with the unsteady Reynolds averaged Navier-Stokes method (URANS), and the obtained pressure spectra are compared with the experimental results.     

A gas‐kinetic scheme for the simulation of turbulent flows on unstructured meshes

This paper presents a numerical method for simulating turbulent flows via coupling the Boltzmann BGK equation with Spalart–Allmaras one equation turbulence model. Both the Boltzmann BGK equation and the turbulence model equation are carried out using the finite volume method on unstructured meshes, which is different from previous works on structured grid. The application of the gas‐kinetic scheme is extended to the simulation of turbulent flows with arbitrary geometries. The adaptive mesh refinement technique is also adopted to reduce the computational cost and improve the efficiency of meshes. To organize the unstructured mesh data structure efficiently, a non‐manifold hybrid mesh data structure is extended for polygonal cells. Numerical experiments are performed on incompressible flow over a smooth flat plate and compressible turbulent flows around a NACA 0012 airfoil using unstructured hybrid meshes. These numerical results are found to be in good agreement with experimental data and/or other numerical solutions, demonstrating the applicability of the proposed method to simulate both subsonic and transonic turbulent flows. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling of Internal Reacting Flows and External Static Stall Flows Using RANS and PRNS

The reacting flow in a research lean direct injection (LDI) hydrogen combustor and the static stall of NACA0012 airfoil were simulated using both Reynolds averaged Navier–Stokes (RANS) and partially resolved numerical simulation (PRNS) approaches. The concept and the main features of the PRNS approach are briefly described. The PRNS basic equations are grid independent or grid invariant; the subscale models are a dynamic equation system. We consider PRNS as an engineering tool for the very large eddy simulation of complex turbulent flows. Two CFD codes, NCC and Wind-US, with two different subscale models (i.e. two- and one-transport equation models, respectively) are used in the presented PRNS simulations. Based on the comparisons with available experimental data, the numerical results indicate that the PRNS subscale models seem to be able to capture important large scale turbulent structures and to improve the quality of numerical simulations while keeping a relatively low cost comparable to the unsteady RANS simulations.     

A mesh-free radial basis function–based semi-Lagrangian lattice Boltzmann method for incompressible flows

In this paper, a local radial basis function–based semi-Lagrangian lattice Boltzmann method (RBF-SL-LBM) is proposed. This is a mesh-free method that can be used for the simulation of incompressible flows. In this method, the collision step is performed locally, which is the same as in the standard LBM. In the meanwhile, the steaming step is solved in a semi-Lagrangian framework. The distribution functions at the departure points, which may be not the grid points in general, are computed by the local radial basis function interpolation. Several numerical tests are conducted to validate the present method, including the lid-driven cavity flow, the steady and unsteady flow past a circular cylinder, and the flow past an NACA0012 airfoil. The present results are in good agreement with those published in the previous literature, which demonstrates the capability of RBF-SL-LBM for the simulation of incompressible flows.     

无网格算法在多段翼型流动计算中的应用

研究了一种求解欧拉方程的无网格算法，发展出了一套布点及点云自动生成的方法；在点云离散的基础上，采用最小二乘法求解矛盾方程的方法来求取空间导数，进而获得数值通量；采用四步龙格-库塔方法进行时间推进，并引入当地时间步长和残值光顺等加速收敛措施。通过对NA-CA0012翼型的跨音速流动和多段翼型复杂绕流的数值模拟，验证了上述无网格算法的正确性和实用性。     

动网格生成技术及非定常计算方法进展综述

对应用于飞行器非定常运动的数值计算方法(包括动态网格技术和相应的数值离散格式)进行了综述.根据网格拓扑结构的不同,重点论述了基于结构网格的非定常计算方法和基于非结构/混合网格的非定常计算方法,比较了各种方法的优缺点.在基于结构网格的非定常计算方法中,重点介绍了刚性运动网格技术、超限插值动态网格技术、重叠动网格技术、滑移动网格技术等动态结构网格生成方法,同时介绍了惯性系和非惯性系下的控制方程,讨论了非定常时间离散方法、动网格计算的几何守恒律等问题.在基于非结构/混合网格的非定常计算方法中,重点介绍了重叠非结构动网格技术、重构非结构动网格技术、变形非结构动网格技术以及变形/重构耦合动态混合网格技术等方法,以及相应的计算格式,包括非定常时间离散、几何守恒律计算方法、可压缩和不可压缩非定常流动的计算方法、各种加速收敛技术等.在介绍国内外进展的同时,介绍了作者在动态混合网格生成技术和相应的非定常方法方面的研究与应用工作.